Large Number Formats

Source - https://xkcd.com/2319/

See, it's funny because the distance from Earth to Jupiter (a constantly changing distance, admittedly) is a really big number (citation needed), and really big numbers can be written in different ways.

First, as a normal person would write the number, it's 25,259,974,097,204 inches (not the most practical of units for this) from Earth to Jupiter. Admittedly, if we're using inches, your location on Earth very much matters as to the precision (14 significant figures???) of that measurement.

Rounding that off, that would be about 25 trillion inches. That's the same number but to only two digits of precision.

In British numbers - at least a while ago - a billion meant a 'million million' whereas in American English a billion meant a 'thousand million'. Hence the confusion there.

The 2.526 x 10¹³ is the same but to four significant digits and using proper scientific notation (something some of my students struggle with but that I continue to insist that they use, especially when we're dealing with numbers of atoms).

The scientist trying to avoid rounding up just kept everything until he or she got to a zero. Forget sig figs.

The software developer doesn't have superscripts. I don't get that, but I see students try to write that all the time - especially if they're just using a calculator with an E display.

I really don't understand floating point numbers, though I understand that programmers do.

The astronomer only cares about the order of magnitude involved. Everything else is just rounding at that level.

The set theorist includes every number underneath the actual number starting with the empty set.

And Abe would just divide the number by twenty and add the remainder. 

See, funny...